OFFSET
0,2
COMMENTS
The sequence { a(n) - n, n >= 0 } has no upper limit (this because the sequence A065363 can be positive on arbitrarily large intervals).
EXAMPLE
For n = 9:
- the orbit of 9 contains the following values:
k v bter(v) ds(v)
- -- ------- -----
0 9 100 1
1 10 101 2
2 12 110 2
3 14 1TTT -2
4 12 110 2
- so a(9) = max({ 9, 10, 12, 14 }) = 14.
MATHEMATICA
f[n_] := n + Total[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[n, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, k - 3, z}]]; Array[Max@ NestWhileList[f, #, UnsameQ, All] &, 67, 0] (* Michael De Vlieger, Jan 15 2022 *)
PROG
(PARI) b(n) = my (v=n, d); while (n, n=(n-d=[0, 1, -1][1+n%3])/3; v+=d); v
a(n) = my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=b(n)); s[#s]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 10 2022
STATUS
approved